Linked Questions
20 questions linked to/from Risk of extinction of Schrödinger's cats
4
votes
1
answer
146
views
Probability mass function with variable probability? [duplicate]
I would like to calculate the probability of a certain result coming out at least 'x' times in 'n' attempts when the probability of result varies on every attempt; all attempts are independent events.
...
- 165
2
votes
1
answer
340
views
Probability distribution for varying probabilities in R [duplicate]
I'd like to plot the probability distribution for a set of binomial trials in R, the catch is that each trial has an independent probability of success (which I have in vector form).
So, in R if I ...
- 21
1
vote
1
answer
282
views
How can I efficiently approximate the sum of Bernoulli random variables for any number of summands in partial sum? [duplicate]
I have almost the same question as:
How can I efficiently model the sum of Bernoulli random variables?
But:
(1) The number of random variables for summation is ~ N=20 (case 1) or N=90 (case 2).
(2) $...
- 41
1
vote
0
answers
13
views
The probability of at least N positive outcomes where all experiments have different probabilities [duplicate]
Let's say we bet on 10 different soccer matches. The probability of our team winning, for each game, is 0.17, 0.78, 0.41, 0.79, 0.47, 0.08, 0.29, 0.30, 0.35, and 0.54. What is the probability of ...
- 173
1
vote
0
answers
10
views
General way to describe dot product of N different random variables [duplicate]
I'm a novice to DS, so feel free to correct me.
Imagine we have $N$ biased coins each with different probability of getting heads (which are known to us prior). What's the probability of getting $k$ ...
- 111
43
votes
9
answers
15k
views
How can I efficiently model the sum of Bernoulli random variables?
I am modeling a random variable ($Y$) which is the sum of some ~15-40k independent Bernoulli random variables ($X_i$), each with a different success probability ($p_i$). Formally, $Y=\sum X_i$ where $\...
- 1,321
60
votes
5
answers
43k
views
Probability distribution for different probabilities
If I wanted to get the probability of 9 successes in 16 trials with each trial having a probability of 0.6 I could use a binomial distribution. What could I use if each of the 16 trials has a ...
- 803
20
votes
2
answers
44k
views
Sum of Bernoulli variables with different success probabilities [duplicate]
Let $x_i$ be independent Bernoulli random variables with success probabilities $p_i$. That is, $x_i=1$ with probability $p_i$ and $x_i=0$ with probability $1-p_i$.
Is there a closed expression or an ...
- 4,552
8
votes
1
answer
9k
views
Efficient convolution (in R)
I want to calculate/evaluate the convolution
$$g(x)=\int_D f(x-t) \phi(t) dt,$$
where $f$ is a density and $\phi$ is a smooth function with compact support $D$. The convolution is not available in ...
- 83
2
votes
2
answers
2k
views
Distribution of a linear combination of Bernoulli random variables?
I am trying to calculate the expectation of absolute value of a linear combination of independent Bernoulli random variables, $E(|a_1x_1 + a_2x_2 + ...+ a_nx_n|)$. In particular, $(a_1, ..., a_n)$ are ...
- 23
5
votes
1
answer
660
views
Probability of at least $k$ Bernoulli successes with varying probabilities conditional on an event
Suppose a female in a given species has, on a given year $x$, PMF $Bernoulli(f(x))$ of finding a mate given she doesn't yet have one. Once she finds a mate, she doesn't need another.
This same ...
- 210
5
votes
2
answers
257
views
Estimate Number of Party Guests
You are throwing a party and want to know how many guests you can expect.
You are inviting $N$ persons, each person has a probability $x_i$, $ 1 \leq i \leq N$ of showing up and $x_i$ is between 0 and ...
- 267
1
vote
1
answer
926
views
Probability of completing N events
I'd like to calculate the probability that at least N independent events out of a set of M events complete successfully. Each event Ei has a probability of success of Pi.
For example, if there are ...
- 13
2
votes
1
answer
542
views
How to obtain the density of a sum of independent discrete random variables?
Let's $X_1, X_2, ..., X_n$, $n=1,2,...$ are independent discrete random variables.
It is necessary to find the distribution law of the their sum:
$p(k) =P(X_1 + X_2 + ... + X_n = k), k=0, 1, 2, ... $
...
- 856
4
votes
2
answers
296
views
Calculate percentiles of probabilistic functions
For easier understanding, let's assume we talk about sport betting. There are 3 independent games with team_A winning with a probability of 70%, 50%, 10% respectively. Each bet has its odds (odds_1, ...
- 558